The Quantum Reduced Action In Higher Dimensions

Details The Quantum Reduced Action In Higher Dimensions The Quantum Reduced Action In Higher Dimensions

2009-06-07

arxiv.org/abs/0906.1362v1

Int. J. Theor. Phys. 48 (2009) 913-923

Physics

Quantum Physics

12 pages, no figure

Scientific paper

The solution with respect to the reduced action of the one-dimensional stationary quantum Hamilton-Jacobi equation is well known in the literature. The extension to higher dimensions in the separated variable case was proposed in contradictory formulations. In this paper we provide new insights into the construction of the reduced action. In particular, contrary to the classical mechanics case, we analytically show that the reduced action constructed as a sum of one variable functions does not contain a complete information about the quantum motion. In the same context, we also make some observations about recent results concerning quantum trajectories. Finally, we will examine the conditions in which microstates appear even in the case where the wave function is complex.

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